Abstract

Using GEPD data from Peru, this paper examines the psychometric properties of the mathematics portion of the teacher assessment module. We estimate a two parameter logistic (2PL) item response theory (IRT) model. We produce item characteristic curves (ICC) and test characteristic curves from this model. We then compare our results to data from a similar assessment used in the Service Delivery Indicators project in several Sub-Sahara African countries using an item equating approach.

Takeaways:

Methodological Approach

We use a model from Item Response Theory (IRT) to examine the functioning of the teacher knowledge test items for Language and Mathematics. The model used is the Two Parameter Logistic (2PL), which allows for items with binary responses (Correct/Incorrect) The model is as follows for item i and person j:

\[ P(u_{ij}=1|\theta_j,\omega)=\frac{exp(a_i(\theta_j - b_{i} ))}{1+exp(a_i(\theta_j - b_{i} ))} \]

Summary Statistics of Data

Before estimating the model, we begin by examining summary statistics and missing values in our item response data. To begin, we will show summary statistics of the fraction correct on the language and math sections of the examination, as well as the fraction correct on broad sub-domains.

The sub-domains for the language section are:

The sub-domains for the math section are:

## Joining, by = "name"
Table 1: Summary Statistics of Fraction Correct on Language Assessment Domains for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
cloze Cloze task 0.5 0.31 0 0.27 0.55 0.73 1 358 0 ▇▁▅▂▅▇▃▅
correct_letter Correct the letter 0.26 0.2 0 0.087 0.24 0.39 0.91 358 0 ▇▇▅▅▃▁▁▁
grammar Grammar task 0.77 0.27 0 0.67 0.83 1 1 358 0 ▁▁▁▂▁▃▅▇
literacy_content_knowledge Fraction correct language 0.43 0.18 0 0.3 0.44 0.55 0.88 358 0 ▂▂▇▇▇▆▃▁
read_passage Read the passage 0.77 0.33 0 0.67 1 1 1 358 0 ▁▁▁▁▁▃▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment. 
## Joining, by = "name"
Table 2: Summary Statistics of Fraction Correct on Math Assessment Domains for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
arithmetic_number_relations Arithmetic and number relations 0.61 0.27 0 0.43 0.64 0.86 1 367 0 ▂▃▃▅▂▆▇▅
geometry Geometry 0.63 0.33 0 0.25 0.75 1 1 367 0 ▂▅▁▅▁▅▁▇
interpret_data Interpret Data 0.6 0.31 0 0.4 0.6 0.8 1 367 0 ▃▃▁▅▆▁▇▆
math_content_knowledge Fraction correct math 0.61 0.26 0 0.43 0.65 0.83 1 367 0 ▂▂▃▅▅▆▇▆
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Item Level Summary Statistics

Next, we display summary statistics at the item level for our language and mathematics assessment.

Table 3: Summary Statistics of Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.58 0.49 0 0 1 1 1 358 0 ▆▁▁▁▁▁▁▇
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.76 0.43 0 1 1 1 1 358 0 ▂▁▁▁▁▁▁▇
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.81 0.39 0 1 1 1 1 358 0 ▂▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.86 0.35 0 1 1 1 1 358 0 ▁▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.77 0.42 0 1 1 1 1 358 0 ▂▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.87 0.34 0 1 1 1 1 358 0 ▁▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0.61 0.49 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q2b_cloze Get (b) . 0.16 0.37 0 0 0 0 1 358 0 ▇▁▁▁▁▁▁▂
m5s1q2c_cloze Today there is a (c) big football match at school. 0.63 0.48 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.65 0.48 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q2e_cloze I am (e) scared to go. 0.46 0.5 0 0 0 1 1 358 0 ▇▁▁▁▁▁▁▇
m5s1q2f_cloze Everyone (f) hates me. 0.64 0.48 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q2g_cloze The players want to beat (g) . 0.4 0.49 0 0 0 1 1 358 0 ▇▁▁▁▁▁▁▅
m5s1q2h_cloze
  1. Where do I have to go to school?
0.33 0.47 0 0 0 1 1 358 0 ▇▁▁▁▁▁▁▃
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.3 0.46 0 0 0 1 1 358 0 ▇▁▁▁▁▁▁▃
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.65 0.48 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q2k_cloze Javid, it is (a) half past seven. 0.64 0.48 0 0 1 1 1 358 0 ▅▁▁▁▁▁▁▇
m5s1q3__1 Please indicate how many errors were correctly corrected:error 1 0.1 0.31 0 0 0 0 1 354 4 ▇▁▁▁▁▁▁▁
m5s1q3__10 Please indicate how many errors were correctly corrected:error 10 0.57 0.5 0 0 1 1 1 357 1 ▆▁▁▁▁▁▁▇
m5s1q3__11 Please indicate how many errors were correctly corrected:error 11 0.55 0.5 0 0 1 1 1 357 1 ▆▁▁▁▁▁▁▇
m5s1q3__12 Please indicate how many errors were correctly corrected:error 12 0.38 0.49 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▅
m5s1q3__13 Please indicate how many errors were correctly corrected:error 13 0.05 0.22 0 0 0 0 1 357 1 ▇▁▁▁▁▁▁▁
m5s1q3__14 Please indicate how many errors were correctly corrected:error 14 0.048 0.21 0 0 0 0 1 356 2 ▇▁▁▁▁▁▁▁
m5s1q3__15 Please indicate how many errors were correctly corrected:error 15 0.37 0.48 0 0 0 1 1 356 2 ▇▁▁▁▁▁▁▅
m5s1q3__16 Please indicate how many errors were correctly corrected:error 16 0.28 0.45 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q3__17 Please indicate how many errors were correctly corrected:error 17 0.31 0.46 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q3__18 Please indicate how many errors were correctly corrected:error 18 0.0028 0.053 0 0 0 0 1 356 2 ▇▁▁▁▁▁▁▁
m5s1q3__19 Please indicate how many errors were correctly corrected:error 19 0.056 0.23 0 0 0 0 1 355 3 ▇▁▁▁▁▁▁▁
m5s1q3__2 Please indicate how many errors were correctly corrected:error 2 0.27 0.45 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q3__20 Please indicate how many errors were correctly corrected:error 20 0.15 0.35 0 0 0 0 1 355 3 ▇▁▁▁▁▁▁▂
m5s1q3__21 Please indicate how many errors were correctly corrected:error 21 0.16 0.37 0 0 0 0 1 358 0 ▇▁▁▁▁▁▁▂
m5s1q3__22 Please indicate how many errors were correctly corrected:error 22 0.36 0.48 0 0 0 1 1 356 2 ▇▁▁▁▁▁▁▅
m5s1q3__23 Please indicate how many errors were correctly corrected:error 23 0.28 0.45 0 0 0 1 1 355 3 ▇▁▁▁▁▁▁▃
m5s1q3__3 Please indicate how many errors were correctly corrected:error 3 0.31 0.46 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q3__4 Please indicate how many errors were correctly corrected:error 4 0.3 0.46 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q3__5 Please indicate how many errors were correctly corrected:error 5 0.37 0.48 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▅
m5s1q3__6 Please indicate how many errors were correctly corrected:error 6 0.27 0.44 0 0 0 1 1 356 2 ▇▁▁▁▁▁▁▃
m5s1q3__7 Please indicate how many errors were correctly corrected:error 7 0.24 0.43 0 0 0 0 1 354 4 ▇▁▁▁▁▁▁▂
m5s1q3__8 Please indicate how many errors were correctly corrected:error 8 0.24 0.43 0 0 0 0 1 356 2 ▇▁▁▁▁▁▁▂
m5s1q3__9 Please indicate how many errors were correctly corrected:error 9 0.32 0.47 0 0 0 1 1 357 1 ▇▁▁▁▁▁▁▃
m5s1q4a_passage 4a. Why did the animals huddle together beneath the bushes? 0.79 0.41 0 1 1 1 1 358 0 ▂▁▁▁▁▁▁▇
m5s1q4b_passage 4b. “His big eyes widened like saucers.” What do these words from the story tell 0.82 0.38 0 1 1 1 1 358 0 ▂▁▁▁▁▁▁▇
m5s1q4c_passage 4c. What made the roaring sound in the distance? 0.69 0.46 0 0 1 1 1 357 1 ▃▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 4: Summary Statistics of Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.61 0.49 0 0 1 1 1 367 0 ▅▁▁▁▁▁▁▇
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.3 0.46 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▃
m5s2q11a_number 11a. √(144= )12 0.83 0.38 0 1 1 1 1 367 0 ▂▁▁▁▁▁▁▇
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.75 0.43 0 1 1 1 1 367 0 ▂▁▁▁▁▁▁▇
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.35 0.48 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▅
m5s2q12_number
  1. What is n?
0.41 0.49 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▆
m5s2q13a_geometric 13a. (a) Perimeter: 0.57 0.5 0 0 1 1 1 367 0 ▆▁▁▁▁▁▁▇
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.49 0.5 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▇
m5s2q1a_number 1a. 5/8 +1/4= 6/12 0.42 0.49 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▆
m5s2q1b_number 1b. √36- √9= √27 0.46 0.5 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▇
m5s2q1c_number 1c. 343+215+127= 685 0.87 0.33 0 1 1 1 1 367 0 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.71 0.46 0 0 1 1 1 367 0 ▃▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.7 0.46 0 0 1 1 1 367 0 ▃▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.72 0.45 0 0 1 1 1 367 0 ▃▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.79 0.41 0 1 1 1 1 367 0 ▂▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.45 0.5 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▆
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.38 0.49 0 0 0 1 1 367 0 ▇▁▁▁▁▁▁▅
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.63 0.48 0 0 1 1 1 367 0 ▅▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.9 0.31 0 1 1 1 1 367 0 ▁▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.59 0.49 0 0 1 1 1 367 0 ▆▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.76 0.43 0 1 1 1 1 367 0 ▂▁▁▁▁▁▁▇
m5s2q9a_data 9a. How many people had cats? 0.64 0.48 0 0 1 1 1 367 0 ▅▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.71 0.46 0 0 1 1 1 367 0 ▃▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Inter-Item Correlations

Next we display inter-item correlations for our language and math teacher assessment.

Scree Plots to Test for Number of Dimensions

A “scree” test based on the Parallel Analysis approach is one of the most common tests for assessing the number of dimensions a set of items cover. A scree test plots the eigenvalues of the matrix of inter-item correlations.

## Parallel analysis suggests that the number of factors =  14  and the number of components =  NA

## Parallel analysis suggests that the number of factors =  6  and the number of components =  NA

Plots of Test Information Function and Test Reliability Function

Below we plot the test information and test reliability functions estimated from our 2PL IRT model.

Item Information Functions

Below is a plot of the item information functions for all of our math and language items. Specific items can be displayed by using the filters in the sidebars.

SDI Comparison

Next, we examine how teachers in Peru compare to teachers in other countries that have taken a similar examination. The Service Delivery Indicator survey has been deployed in several countries, mostly in Sub-Saharan Africa. The teacher assessment used is very similar to the one used in the Peru Dashboard survey. In fact, the Peru test instrument was taken directly from the SDI instrument, with a few modifications. A ‘read the passage’ item was added to our instrument, which differs from most SDI assessments. Additionally, two arithmetic and number relations math problems on square roots and adding fractions were added to make our math assessment more difficult.

The list of overlapping items is below.

## [1] "The following items in Language overlapped in SDI and the Dashboard:"
##  [1] "m5s1q1a_grammer" "m5s1q1b_grammer" "m5s1q1c_grammer"
##  [4] "m5s1q1d_grammer" "m5s1q1e_grammer" "m5s1q1f_grammer"
##  [7] "m5s1q2a_cloze"   "m5s1q2b_cloze"   "m5s1q2c_cloze"  
## [10] "m5s1q2d_cloze"   "m5s1q2e_cloze"   "m5s1q2f_cloze"  
## [13] "m5s1q2g_cloze"   "m5s1q2h_cloze"   "m5s1q2i_cloze"  
## [16] "m5s1q2j_cloze"   "m5s1q2k_cloze"
## [1] "The following items in Math overlapped in SDI and the Dashboard:"
##  [1] "m5s2q1c_number"     "m5s2q1d_number"     "m5s2q1e_number"    
##  [4] "m5s2q2_number"      "m5s2q3_number"      "m5s2q4a_number"    
##  [7] "m5s2q4b_number"     "m5s2q5_number"      "m5s2q6_geometric"  
## [10] "m5s2q7_geometric"   "m5s2q8_data"        "m5s2q9a_data"      
## [13] "m5s2q9b_data"       "m5s2q10a_data"      "m5s2q10b_data"     
## [16] "m5s2q11a_number"    "m5s2q11b_number"    "m5s2q11c_number"   
## [19] "m5s2q12_number"     "m5s2q13a_geometric" "m5s2q13b_geometric"

In what follows below, we will compare teacher latent ability scores for Peru using our Dashboard Survey to ability scores from the SDI survey in Kenya, Lao PDR, Madagascar, Morocco, Mozambique, and Tanzania.

Methodology for item equating

In order to equate the ability scores produced using the different instruments, we use an IRT equating method based on the common set of items. We use the ‘equateIRT’ R package to do so. https://cran.r-project.org/web/packages/equateIRT/equateIRT.pdf.

The goal of test equating in our case is to place scores from Dashboard survey and the SDI survey on a common scale, so that we can directly compare teacher latent ability across countries. We use the common set of items, listed above, to do the equating. A direct equating approach is used based on the Stocking-Lord approach.

Summary Statistics of Ability Scores

Below we show the distributions of teacher ability scores based on the IRT model estimates.

## Picking joint bandwidth of 0.168
Table 5: Summary Statistics of Math Assessment Scores for Teachers Across Countries
countryname n mean sd p0 p25 p50 p75 p100 hist
Kenya 1679 0.36 0.83 -2.94 -0.019 0.5 0.9 1.65 ▁▁▁▂▃▆▇▃
Lao PDR 740 -0.0049 0.66 -2.48 -0.45 -0.018 0.44 1.6 ▁▁▂▆▇▇▃▁
Madagascar 2027 -0.29 0.6 -2.44 -0.67 -0.27 0.15 1.38 ▁▁▂▅▇▇▂▁
Morocco 1028 0.62 0.65 -1.76 0.23 0.65 1.05 1.65 ▁▁▁▂▅▇▆▅
Mozambique 670 -1.51 0.94 -2.94 -2.14 -1.58 -0.86 1.65 ▆▇▇▆▅▂▁▁
Peru 367 -0.21 1.01 -2.91 -0.85 -0.087 0.53 1.71 ▁▂▅▅▇▇▆▃
Tanzania 2097 0.17 0.59 -2.94 -0.22 0.18 0.56 1.65 ▁▁▁▂▆▇▅▂ 
## Picking joint bandwidth of 0.15
Table 6: Summary Statistics of Language Assessment Scores for Teachers Across Countries
countryname n mean sd p0 p25 p50 p75 p100 hist
Kenya 1679 0.53 0.69 -2.94 0.17 0.58 0.99 1.76 ▁▁▁▁▃▇▇▅
Lao PDR 740 -0.098 0.72 -2.77 -0.6 -0.1 0.47 0.92 ▁▁▁▂▅▆▅▇
Madagascar 2027 0.14 0.8 -2.77 -0.43 0.27 0.92 1.76 ▁▁▂▃▅▅▇▁
Morocco 1028 -0.79 0.65 -2.58 -1.27 -0.85 -0.36 1.28 ▁▂▆▇▇▃▂▁
Mozambique 670 -0.83 0.71 -2.94 -1.27 -0.84 -0.39 1.76 ▁▂▅▇▆▂▁▁
Peru 358 -0.15 0.59 -1.98 -0.48 -0.099 0.23 1.49 ▁▁▂▅▇▅▂▁
Tanzania 2097 0.098 0.72 -2.94 -0.38 0.13 0.57 1.76 ▁▁▁▃▆▇▅▂

Summary Statistics SDI - Kenya

Table 7: Summary Statistics of Kenya Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.7 0.46 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.91 0.29 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.98 0.14 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.93 0.26 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.91 0.28 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.94 0.23 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0.82 0.38 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2b_cloze Get (b) . 0.86 0.35 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s1q2c_cloze Today there is a (c) big football match at school. 0.62 0.49 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.38 0.48 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▅
m5s1q2e_cloze I am (e) scared to go. 0.24 0.43 0 0 0 0 1 1679 0 ▇▁▁▁▁▁▁▂
m5s1q2f_cloze Everyone (f) hates me. 0.8 0.4 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2g_cloze The players want to beat (g) . 0.73 0.44 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s1q2h_cloze
  1. Where do I have to go to school?
0.64 0.48 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.86 0.35 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s1q2k_cloze Javid, it is (a) half past seven. 0.67 0.47 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m6sa1q1a NA 0.98 0.15 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1b NA 0.97 0.18 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1c NA 0.96 0.2 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa1q1d NA 0.92 0.27 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 8: Summary Statistics of Kenya Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.82 0.39 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.43 0.5 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▆
m5s2q11a_number 11a. √(144= )12 0.89 0.31 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.82 0.38 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.68 0.46 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q12_number
  1. What is n?
0.73 0.45 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q13a_geometric 13a. (a) Perimeter: 0.8 0.4 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.75 0.44 0 0 1 1 1 1679 0 ▃▁▁▁▁▁▁▇
m5s2q1c_number 1c. 343+215+127= 685 0.88 0.32 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.86 0.34 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.87 0.33 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.91 0.29 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.4 0.49 0 0 0 1 1 1679 0 ▇▁▁▁▁▁▁▆
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.51 0.5 0 0 1 1 1 1679 0 ▇▁▁▁▁▁▁▇
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.83 0.37 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.95 0.23 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.93 0.25 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m5s2q9a_data 9a. How many people had cats? 0.62 0.49 0 0 1 1 1 1679 0 ▅▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.77 0.42 0 1 1 1 1 1679 0 ▂▁▁▁▁▁▁▇
m6sa2q1a NA 0.97 0.16 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
m6sa2q1b NA 0.87 0.33 0 1 1 1 1 1679 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Summary Statistics SDI - Mozambique

Table 9: Summary Statistics of Mozambique Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.27 0.44 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.66 0.47 0 0 1 1 1 670 0 ▅▁▁▁▁▁▁▇
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.86 0.35 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.91 0.29 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.9 0.3 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.89 0.31 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. 0.47 0.5 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s1q2b_cloze Get (b) . 0.28 0.45 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s1q2c_cloze Today there is a (c) big football match at school. 0.56 0.5 0 0 1 1 1 670 0 ▆▁▁▁▁▁▁▇
m5s1q2d_cloze Juma: Father, I (d) want not go to school. 0.5 0.5 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s1q2e_cloze I am (e) scared to go. 0.24 0.43 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s1q2f_cloze Everyone (f) hates me. 0.3 0.46 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s1q2g_cloze The players want to beat (g) . 0.3 0.46 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s1q2h_cloze
  1. Where do I have to go to school?
0.082 0.27 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) 0.04 0.2 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. 0.3 0.46 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s1q2k_cloze Javid, it is (a) half past seven. 0.34 0.48 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▅
m6sa1q1a NA 0.95 0.23 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m6sa1q1b NA 0.91 0.28 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m6sa1q1c NA 0.88 0.32 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
m6sa1q1d NA 0.9 0.3 0 1 1 1 1 670 0 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 10: Summary Statistics of Mozambique Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.23 0.42 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.042 0.2 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q11a_number 11a. √(144= )12 0.24 0.43 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.24 0.43 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.1 0.3 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q12_number
  1. What is n?
0.076 0.27 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q13a_geometric 13a. (a) Perimeter: 0.12 0.33 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.099 0.3 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q1c_number 1c. 343+215+127= 685 0.66 0.48 0 0 1 1 1 670 0 ▅▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.54 0.5 0 0 1 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.53 0.5 0 0 1 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.37 0.48 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▅
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.44 0.5 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▆
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.1 0.3 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.088 0.28 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▁
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.26 0.44 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m5s2q6_geometric
  1. How many sides does a triangle have?
0.51 0.5 0 0 1 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.47 0.5 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.22 0.41 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s2q9a_data 9a. How many people had cats? 0.21 0.41 0 0 0 0 1 670 0 ▇▁▁▁▁▁▁▂
m5s2q9b_data 9b. Which animal was the least popular? 0.28 0.45 0 0 0 1 1 670 0 ▇▁▁▁▁▁▁▃
m6sa2q1a NA 0.77 0.42 0 1 1 1 1 670 0 ▂▁▁▁▁▁▁▇
m6sa2q1b NA 0.66 0.47 0 0 1 1 1 670 0 ▅▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.

Summary Statistics SDI - LAO_PDR

Table 11: Summary Statistics of Lao PDR Language Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s1q1a_grammer (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. 0.47 0.5 0 0 0 1 1 690 50 ▇▁▁▁▁▁▁▇
m5s1q1b_grammer (When, If, Because, Although) I was telling the truth, my mother didn’t believe 0.44 0.5 0 0 0 1 1 691 49 ▇▁▁▁▁▁▁▆
m5s1q1c_grammer A person who (which, who, when, may) flies an airplane is a pilot. 0.87 0.34 0 1 1 1 1 713 27 ▁▁▁▁▁▁▁▇
m5s1q1d_grammer My sister likes to read, so (so, although, perhaps, when) I have boug 0.83 0.37 0 1 1 1 1 707 33 ▂▁▁▁▁▁▁▇
m5s1q1e_grammer If I were a doctor, I shall (will, would, shall, am able to) work i 0.88 0.32 0 1 1 1 1 713 27 ▁▁▁▁▁▁▁▇
m5s1q1f_grammer The accident had seen (see, saw, had seen, was seen) by three people 0.81 0.39 0 1 1 1 1 712 28 ▂▁▁▁▁▁▁▇
m5s1q2a_cloze Javid, it is (a) half past seven. NaN NA NA NA NA NA NA 0 740
m5s1q2b_cloze Get (b) . NaN NA NA NA NA NA NA 0 740
m5s1q2c_cloze Today there is a (c) big football match at school. NaN NA NA NA NA NA NA 0 740
m5s1q2d_cloze Juma: Father, I (d) want not go to school. NaN NA NA NA NA NA NA 0 740
m5s1q2e_cloze I am (e) scared to go. NaN NA NA NA NA NA NA 0 740
m5s1q2f_cloze Everyone (f) hates me. NaN NA NA NA NA NA NA 0 740
m5s1q2g_cloze The players want to beat (g) . NaN NA NA NA NA NA NA 0 740
m5s1q2h_cloze
  1. Where do I have to go to school?
NaN NA NA NA NA NA NA 0 740
m5s1q2i_cloze Father: You are going and that is final. I will give you two (i) NaN NA NA NA NA NA NA 0 740
m5s1q2j_cloze have to go to school today. First, you are 40 (j) years old. NaN NA NA NA NA NA NA 0 740
m5s1q2k_cloze Javid, it is (a) half past seven. NaN NA NA NA NA NA NA 0 740
m6sa1q1a NA 0.94 0.25 0 1 1 1 1 731 9 ▁▁▁▁▁▁▁▇
m6sa1q1b NA 0.87 0.33 0 1 1 1 1 706 34 ▁▁▁▁▁▁▁▇
m6sa1q1c NA 0.81 0.39 0 1 1 1 1 718 22 ▂▁▁▁▁▁▁▇
m6sa1q1d NA 0.96 0.2 0 1 1 1 1 716 24 ▁▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher language assessment.
Table 12: Summary Statistics of Lao PDR Math Assessment Items for Teachers
Item Label Mean Std Dev Min 25th Percentile Median 75th Percentile Max # Complete Cases # Missing Cases Histogram
m5s2q10a_data 10a. Look at the graph. How far has Joe ridden after 6 hours? 0.68 0.47 0 0 1 1 1 358 382 ▃▁▁▁▁▁▁▇
m5s2q10b_data 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? 0.41 0.49 0 0 0 1 1 245 495 ▇▁▁▁▁▁▁▆
m5s2q11a_number 11a. √(144= )12 0.82 0.38 0 1 1 1 1 198 542 ▂▁▁▁▁▁▁▇
m5s2q11b_number 11b. 12.15-11.83= 0.32 0.78 0.41 0 1 1 1 1 278 462 ▂▁▁▁▁▁▁▇
m5s2q11c_number 11c. 3/4÷7/8= 21/32 0.46 0.5 0 0 0 1 1 191 549 ▇▁▁▁▁▁▁▇
m5s2q12_number
  1. What is n?
0.41 0.49 0 0 0 1 1 188 552 ▇▁▁▁▁▁▁▆
m5s2q13a_geometric 13a. (a) Perimeter: 0.26 0.44 0 0 0 1 1 207 533 ▇▁▁▁▁▁▁▃
m5s2q13b_geometric 13b. (b) Area: 90 cm2 0.69 0.46 0 0 1 1 1 186 554 ▃▁▁▁▁▁▁▇
m5s2q1c_number 1c. 343+215+127= 685 0.89 0.31 0 1 1 1 1 732 8 ▁▁▁▁▁▁▁▇
m5s2q1d_number 1d. 72÷9= 7 0.9 0.3 0 1 1 1 1 712 28 ▁▁▁▁▁▁▁▇
m5s2q1e_number 1e. 37×13 = 3711 0.86 0.34 0 1 1 1 1 721 19 ▁▁▁▁▁▁▁▇
m5s2q2_number
  1. Which two numbers add up to make 0.81?
0.76 0.43 0 1 1 1 1 616 124 ▂▁▁▁▁▁▁▇
m5s2q3_number
  1. Circle the one that gives the smallest answer?
0.87 0.34 0 1 1 1 1 656 84 ▁▁▁▁▁▁▁▇
m5s2q4a_number 4a. Complete these fractions so that they are equivalent 0.69 0.46 0 0 1 1 1 443 297 ▃▁▁▁▁▁▁▇
m5s2q4b_number 4b. Complete these fractions so that they are equivalent 0.63 0.48 0 0 1 1 1 436 304 ▅▁▁▁▁▁▁▇
m5s2q5_number
  1. 2 exercise books cost 14 Kips. What is the cost of 15 exercise books?
0.66 0.48 0 0 1 1 1 603 137 ▅▁▁▁▁▁▁▇
m5s2q6_geometric
  1. How many sides does a triangle have?
0.93 0.26 0 1 1 1 1 639 101 ▁▁▁▁▁▁▁▇
m5s2q7_geometric
  1. Lines that cannot meet are lines
0.72 0.45 0 0 1 1 1 602 138 ▃▁▁▁▁▁▁▇
m5s2q8_data
  1. What time did Chanla arrive?
0.6 0.49 0 0 1 1 1 537 203 ▆▁▁▁▁▁▁▇
m5s2q9a_data 9a. How many people had cats? 0.79 0.41 0 1 1 1 1 475 265 ▂▁▁▁▁▁▁▇
m5s2q9b_data 9b. Which animal was the least popular? 0.8 0.4 0 1 1 1 1 408 332 ▂▁▁▁▁▁▁▇
m6sa2q1a NA 0.99 0.11 0 1 1 1 1 724 16 ▁▁▁▁▁▁▁▇
m6sa2q1b NA 0.85 0.36 0 1 1 1 1 736 4 ▂▁▁▁▁▁▁▇
Note:
Summary table shows unweighted summary statistics from teacher math assessment.